Artículos de revista DIMI - MIIS Aldizkari artikuluak

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Open Access
Analysis of radio wave propagation for ISM 2.4 GHz wireless sensor networks in inhomogeneous vegetation environments
(MDPI, 2014) Azpilicueta Fernández de las Heras, Leyre; López Iturri, Peio; Aguirre Gallego, Erik; Mateo Zozaya, Ignacio; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniaritza Elektrikoa eta Elektronikoa; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
The use of wireless networks has experienced exponential growth due to the improvements in terms of battery life and low consumption of the devices. However, it is compulsory to conduct previous radio propagation analysis when deploying a wireless sensor network. These studies are necessary to perform an estimation of the range coverage, in order to optimize the distance between devices in an actual network deployment. In this work, the radio channel characterization for ISM 2.4 GHz Wireless Sensor Networks (WSNs) in an inhomogeneous vegetation environment has been analyzed. This analysis allows designing environment monitoring tools based on ZigBee and WiFi where WSN and smartphones cooperate, providing rich and customized monitoring information to users in a friendly manner. The impact of topology as well as morphology of the environment is assessed by means of an in-house developed 3D Ray Launching code, to emulate the realistic operation in the framework of the scenario. Experimental results gathered from a measurement campaign conducted by deploying a ZigBee Wireless Sensor Network, are analyzed and compared with simulations in this paper. The scenario where this network is intended to operate is a combination of buildings and diverse vegetation species. To gain insight in the effects of radio propagation, a simplified vegetation model has been developed, considering the material parameters and simplified geometry embedded in the simulation scenario. An initial location-based application has been implemented in a real scenario, to test the functionality within a context aware scenario. The use of deterministic tools can aid to know the impact of the topological influence in the deployment of the optimal Wireless Sensor Network in terms of capacity, coverage and energy consumption, making the use of these systems attractive for multiple applications in inhomogeneous vegetation environments.
Open Access
Analysis of wireless sensor network topology and estimation of optimal network deployment by deterministic radio channel characterization
(MDPI, 2015) Aguirre Gallego, Erik; López Iturri, Peio; Azpilicueta Fernández de las Heras, Leyre; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniería Matemática e Informática; Ingeniaritza Elektrikoa eta Elektronikoa; Matematika eta Informatika Ingeniaritza
One of the main challenges in the implementation and design of context-aware scenarios is the adequate deployment strategy for Wireless Sensor Networks (WSNs), mainly due to the strong dependence of the radiofrequency physical layer with the surrounding media, which can lead to non-optimal network designs. In this work, radioplanning analysis for WSN deployment is proposed by employing a deterministic 3D ray launching technique in order to provide insight into complex wireless channel behavior in context-aware indoor scenarios. The proposed radioplanning procedure is validated with a testbed implemented with a Mobile Ad Hoc Network WSN following a chain configuration, enabling the analysis and assessment of a rich variety of parameters, such as received signal level, signal quality and estimation of power consumption. The adoption of deterministic radio channel techniques allows the design and further deployment of WSNs in heterogeneous wireless scenarios with optimized behavior in terms of coverage, capacity, quality of service and energy consumption.
Open Access
Analytic formulas for the evaluation of the Pearcey integral
(American Mathematical Society, 2017) López García, José Luis; Pagola Martínez, Pedro Jesús; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We can find in the literature several convergent and/or asymptotic expansions of the Pearcey integral P(x, y) in different regions of the complex variables x and y, but they do not cover the whole complex x and y planes. The purpose of this paper is to complete this analysis giving new convergent and/or asymptotic expansions that, together with the known ones, cover the evaluation of the Pearcey integral in a large region of the complex x and y planes. The accuracy of the approximations derived in this paper is illustrated with some numerical experiments. Moreover, the expansions derived here are simpler compared with other known expansions, as they are derived from a simple manipulation of the integral definition of P(x, y).
Open Access
Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter
(Shanghai Normal University, 2018) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
In previous papers [6–8,10], we derived convergent and asymptotic expansions of solutions of second order linear differential equations with a large parameter. In those papers we generalized and developed special cases not considered in Olver’s theory [Olver, 1974]. In this paper we go one step forward and consider linear differential equations of the third order: y ′′′ +aΛ2y′ +bΛ3y = f(x)y′ +g(x)y, with a, b ∈ C fixed, f′ and g continuous, and Λ a large positive parameter. We propose two different techniques to handle the problem: (i) a generalization of Olver’s method and (ii) the transformation of the differential problem into a fixed point problem from which we construct an asymptotic sequence of functions that converges to the unique solution of the problem. Moreover, we show that this second technique may also be applied to nonlinear differential equations with a large parameter. As an application of the theory, we obtain new convergent and asymptotic expansions of the Pearcey integral P(x, y) for large |x|.
Open Access
Asymptotic behaviour of the Urbanik semigroup
(Elsevier, 2015) Berg, Christian; López García, José Luis; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We revisit the product convolution semigroup of probability densities ec(t); c > 0 on the positive half-line with moments (n!)c and determine the asymptotic behaviour of ec for large and small t > 0. This shows that (n!)c is indeterminate as Stieltjes moment sequence if and only if c > 2. When c is a natural number ec is a Meijer-G function. From the results about ec we obtain the asymptotic behaviour at 1 of the convolution roots of the Gumbel distribution.
Open Access
The asymptotic expansion of the swallowtail integral in the highly oscillatory region
(Elsevier, 2018) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
The mathematical models of many short wavelength phenomena, specially wave propagation and optical diffraction, contain, as a basic ingredient, oscillatory integrals with several nearly coincident stationary phase or saddle points. The uniform approximation of those integrals can be expressed in terms of certain canonical integrals and their derivatives [2,16]. The importance of these canonical diffraction integrals is stressed in [14] by means of the following sentence: The role played by these canonical diffraction integrals in the analysis of caustic wave fields is analogous to that played by complex exponentials in plane wave theory. Apart from their mathematical importance in the uniform asymptotic approximation of oscillatory integrals [12], the canonical diffraction integrals have physical applications in the description of surface gravity waves [11], [17], bifurcation sets, optics, quantum mechanics, chemical physics [4] and acoustics (see [1], Section 36.14 and references there in). To our knowledge, the first application of this family of integrals traces back to the description of the disturbances on a water surface produced, for example, by a traveling ship. These disturbances form a familiar pattern of bow and stern waves which was first explained mathematically by Lord Kelvin [10] using these integrals.
Open Access
Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge–Kutta–Nyström methods
(Elsevier, 2016) Moreta, M. Jesús; Bujanda Cirauqui, Blanca; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
We study some of the main features of Fractional Step Runge–Kutta–Nyström methods when they are used to integrate Initial–Boundary Value Problems of second order in time, in combination with a suitable spatial discretization. We focus our attention on the order reduction phenomenon, which appears if classical boundary conditions are taken at the internal stages. This drawback is specially hard when time dependent boundary conditions are considered. In this paper we present an efficient technique, very simple and computationally cheap, which allows us to avoid the order reduction; such technique consists in modifying the boundary conditions for the internal stages of the method.
Open Access
Basketball player on-body biophysical and environmental parameter monitoring based on wireless sensor network integration
(IEEE, 2021) Picallo Guembe, Imanol; López Iturri, Peio; Astrain Escola, José Javier; Aguirre Gallego, Erik; Azpilicueta Fernández de las Heras, Leyre; Celaya Echarri, Mikel; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Matematika eta Informatika Ingeniaritza; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren; Institute of Smart Cities - ISC; Ingeniería Matemática e Informática; Ingeniería Eléctrica, Electrónica y de Comunicación
Sport activities have benefited in recent years from the progressive adoption of different technological assets in order to improve individual as well as group training, collect different statistics or enhance the spectator experiences. The progressive adoption of Internet of Things paradigms can also be considered within the scope of sport activities, providing high levels of user interactivity as well as enabling cloud-based data storage and processing. In this work, a system for monitoring biophysical, kinematic and environmental parameters within the development of basketball training is presented. A set of on-body nodes with multiple sensors and wireless body area network capabilities have been designed, implemented and tested under real training conditions during a match. Wireless channel analysis results have been obtained with the aid of in house implemented deterministic 3D ray launching algorithm, providing accurate coverage/capacity estimations in relation with human body consideration in the field as well as in the stadium. Measurement results give relevant information in relation with individual player characteristics as well as with team characteristics, providing a flexible tool to improve training development of basketball.
Open Access
Challenges in wireless system integration as enablers for indoor context aware environments
(MDPI, 2017) López Iturri, Peio; Aguirre Gallego, Erik; Azpilicueta Fernández de las Heras, Leyre; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniaritza Elektrikoa eta Elektronikoa; Matematika eta Informatika Ingeniaritza; Institute of Smart Cities - ISC; Ingeniería Eléctrica y Electrónica; Ingeniería Matemática e Informática
The advent of fully interactive environments within Smart Cities and Smart Regions requires the use of multiple wireless systems. In the case of user-device interaction, which finds multiple applications such as Ambient Assisted Living, Intelligent Transportation Systems or Smart Grids, among others, large amount of transceivers are employed in order to achieve anytime, anyplace and any device connectivity. The resulting combination of heterogeneous wireless network exhibits fundamental limitations derived from Coverage/Capacity relations, as a function of required Quality of Service parameters, required bit rate, energy restrictions and adaptive modulation and coding schemes. In this context, inherent transceiver density poses challenges in overall system operation, given by multiple node operation which increases overall interference levels. In this work, a deterministic based analysis applied to variable density wireless sensor network operation within complex indoor scenarios is presented, as a function of topological node distribution. The extensive analysis derives interference characterizations, both for conventional transceivers as well as wearables, which provide relevant information in terms of individual node configuration as well as complete network layout.
Open Access
Characterization of wireless channel impact on wireless sensor network performance in public transportation buses
(IEEE, 2015) Azpilicueta Fernández de las Heras, Leyre; López Iturri, Peio; Aguirre Gallego, Erik; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Zubiri Segura, Cristóbal; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniería Matemática e Informática; Ingeniaritza Elektrikoa eta Elektronikoa; Matematika eta Informatika Ingeniaritza
Wireless communications systems are growing rapidly during the last two decades and they are gaining a significant role for multiple communication tasks within public transportation buses. In this work, the impact of topology and morphology of different types of urban buses is analyzed with the aid of an in-house developed 3D Ray Launching code and compared with on-board measurements of a deployed Wireless Sensor Network. The presence of human beings has been taken into account, showing a significant influence in the signal attenuation in the case of considering persons. In addition, the statistical analysis of simulation results considering both large and small-scale fading has been performed, providing good agreement with statistics for typical indoor environments. In addition, a Wireless Sensor Network has been programmed and deployed within the buses in order to analyze topological impact with overall system performance, with the aim of minimizing the energy consumption as well as non-desired interference levels. The use of deterministic techniques destined to consider the inherent complexity of the buses can aid in wireless system planning in order to minimize power consumption and increase overall system capacity.
Open Access
Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements
(Springer US, 2016) Higueras Sanz, Inmaculada; Roldán Marrodán, Teodoro; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Space discretization of some time-dependent partial differential equations gives rise to systems of ordinary differential equations in additive form whose terms have different stiffness properties. In these cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be used for the non-stiff part of the problem. However, for systems with a large number of equations, memory storage requirement is also an important issue. When the high dimension of the problem compromises the computer memory capacity, it is important to incorporate low memory usage to some other properties of the scheme. In this paper we consider Additive Semi-Implicit Runge-Kutta (ASIRK) methods, a class of implicitexplicit Runge-Kutta methods for additive differential systems. We construct two second order 3-stage ASIRK schemes with low-storage requirements. Having in mind problems with stiffness parameters, besides accuracy and stability properties, we also impose stiff accuracy conditions. The numerical experiments done show the advantages of the new methods.
Open Access
Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
(Rocky Mountain Mathematics Consortium, 2015) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
This paper continues the investigation initiated in [Lopez, 2013]. We consider the asymptotic method designed by F. Olver [Olver, 1974] for linear differential equations of the second order containing a large (asymptotic) parameter . We consider here the second and third cases studied by Olver: differential equations with a turning point (second case) or a singular point (third case). It is well-known that his method gives the Poincar´e-type asymptotic expansion of two independent solutions of the equation in inverse powers of . In this paper we add initial conditions to the differential equation and consider the corresponding initial value problem. By using the Green function of an auxiliary problem, we transform the initial value problem into a Volterra integral equation of the second kind. Then, using a fixed point theorem, we construct a sequence of functions that converges to the unique solution of the problem. This sequence has also the property of being an asymptotic expansion for large (not of Poincar´e-type) of the solution of the problem. Moreover, we show
Open Access
Convergent and asymptotic expansions of the Pearcey integral
(Elsevier, 2015) López García, José Luis; Pagola Martínez, Pedro Jesús; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of complexity. Most of them are based in analytic, in particular asymptotic, techniques applied to the integral definition of P(x; y). In this paper we consider a different method: the iterative technique used for differential equations in [Lopez, 2012]. Using this technique in a differential equation satisfied by P(x; y) we obtain a new convergent expansion analytically simple that is valid for any complex x and y and has an asymptotic property when |x|→ ∞ uniformly for y in bounded sets. The accuracy of the approximation is illustrated with some numerical experiments and compared with other expansions given in the literature.
Open Access
Convergent and asymptotic methods for second-order difference equations with a large parameter
(Springer, 2018) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find the asymptotic behavior for large |Λ|of the solutions of this equation: (i) an iterative method based on a fixed point method and (ii) a discrete version of Olver’s method for second-order linear differential equations. Both methods provide an asymptotic expansion of every solution of this equation. The expansion given by the first method is also convergent and may be applied to nonlinear problems. Bounds for the remainders are also given. We illustrate the accuracy of both methods for the modified Bessel functions and the associated Legendre functions of the first kind.
Open Access
Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials
(Cambridge University Press, 2004) López García, José Luis; Temme, Nico M.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of functions that are special cases of the given polynomials. The method is based on expanding integrals in one or two points of the complex plane, these points being saddle points of the phase functions of the integrands.
Open Access
Convergent expansions of the Bessel functions in terms of elementary functions
(Springer US, 2018) López García, José Luis; Pagola Martínez, Pedro Jesús; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of (sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives of (1−cos z)/z, derivatives of (1 − e−z)/z and (2ν, z). Both expansions hold uniformly in z in any fixed horizontal strip and are accompanied by error bounds. The accuracy of the approximations is illustrated with some numerical experiments.
Open Access
Convergent expansions of the incomplete gamma functions in terms of elementary functions
(World Scientific Publishing, 2017) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from below. These expansions, multiplied by ez, are expansions of ezz−aγ(a,z) uniformly convergent in z with Rz bounded from above. The expansions are accompanied by realistic error bounds.
Open Access
Decoupling mixed finite elements on hierarchical triangular grids for parabolic problems
(Elsevier, 2018) Arrarás Ventura, Andrés; Portero Egea, Laura; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a regular refinement process inside each of the initial coarse elements. If these elements are considered as subdomains, we can formulate a non-overlapping domain decomposition method based on the lowest-order Raviart–Thomas elements, properly enhanced with Lagrange multipliers on the boundaries of each subdomain (excluding the Dirichlet edges). A suitable choice of mixed finite element spaces and quadrature rules yields a cell-centered scheme for the pressures with a local 10-point stencil. The resulting system of differential-algebraic equations is integrated in time by the Crank–Nicolson method, which is known to be a stiffly accurate scheme. As a result, we obtain independent subdomain linear systems that can be solved in parallel. The behavior of the algorithm is illustrated on a variety of numerical experiments.
Open Access
Design and performance analysis of wireless body area networks in complex indoor e-Health hospital environments for patient remote monitoring
(SAGE, 2016) Aguirre Gallego, Erik; López Iturri, Peio; Azpilicueta Fernández de las Heras, Leyre; Rivarés Garasa, Carmen; Astrain Escola, José Javier; Villadangos Alonso, Jesús; Falcone Lanas, Francisco; Ingeniería Eléctrica y Electrónica; Ingeniaritza Elektrikoa eta Elektronikoa; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
In this article, the design and performance analysis of wireless body area network–based systems for the transmission of medical information readable in an android-based application deployed within complex indoor e-Health scenarios is presented. The scenario under analysis is an emergency room area, where a patient is being monitored remotely with the aid of wearable wireless sensors placed at different body locations. Due to the advent of Internet of Things, in the near future a cloud of a vast number of wireless devices will be operating at the same time, potentially interfering one another. Ensuring good performance of the deployed wireless networks in this kind of environment is mandatory and obtaining accurate radio propagation estimations by means of a computationally efficient algorithm is a key issue. For that purpose, an in-house three-dimensional ray launching algorithm is employed, which provides radio frequency power distribution values, power delay profiles, and delay spread values for the complete volume of complex indoor scenarios. Using this information together with signal-to-noise estimations and link budget calculations, the most suitable wireless body area network technology for this context is chosen. Additionally, an in-house developed human body model has been developed in order to model the impact of the presence of monitored patients. A campaign of measurements has been carried out in order to validate the obtained simulation results. Both the measurements and simulation results illustrate the strong influence of the presented scenario on the overall performance of the wireless body area networks: losses due to material absorption and the strong influence of multipath components due to the great number of obstacles and the presence of persons make the use of the presented method very useful. Finally, an android-based application for the monitoring of patients is presented and tested within the emergency room scenario, providing a flexible solution to increase interactivity in health service provision.
Open Access
Dynamics of axially symmetric perturbed Hamiltonians in 1:1:1 resonance
(Springer, 2018) Carrasco, Dante; Palacián Subiela, Jesús Francisco; Vidal Díaz, Claudio; Vidarte, Jhon; Yanguas Sayas, Patricia; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática
We study the dynamics of a family of perturbed three-degree-of-freedom Hamiltonian systems which are in 1:1:1 resonance. The perturbation consists of axially symmetric cubic and quartic arbitrary polynomials. Our analysis is performed by normalisation, reduction and KAM techniques. Firstly, the system is reduced by the axial symmetry, and then, periodic solutions and KAM 3-tori of the full system are determined from the relative equilibria. Next, the oscillator symmetry is extended by normalisation up to terms of degree 4 in rectangular coordinates; after truncation of higher orders and reduction to the orbit space, some relative equilibria are established and periodic solutions and KAM 3-tori of the original system are obtained. As a third step, the reduction in the two symmetries leads to a one-degree-of-freedom system that is completely analysed in the twice reduced space. All the relative equilibria together with the stability and parametric bifurcations are determined. Moreover, the invariant 2-tori (related to the critical points of the twice reduced space), some periodic solutions and the KAM3-tori, all corresponding to the full system, are established. Additionally, the bifurcations of equilibria occurring in the twice reduced space are reconstructed as quasi-periodic bifurcations involving 2-tori and periodic solutions of the full system.